MUMBAI—India's currency hit a record low against the dollar, on rising concerns over a widening trade imbalance and the pace of promised economic steps.

While a rise in the dollar triggered Monday's milestone, emerging-market investors attributed the broader weakness in the Indian rupee to the country's ballooning current-account deficit. They say the deficit has become emblematic of the troubles in Asia's second-largest economy, which is suffering from slowing growth and high inflation. India's exports remain sluggish because...